Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of Elliptic Curves.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.- Integral Points on Elliptic Curves.-Computing the Mordell Weil Group.- Appendix A: Elliptic Curves in Characteristics.-Appendix B: Group Cohomology (H0 and H1).

https://www.pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf

The Arithmetic of Elliptic Curves

© Publications mathématiques de l’I.H.É.S., 1992, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » ( http://www. ihes.fr/IHES/Publications/Publications.html), implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

/pdf/higgs-bundles-and-local-systems-47a3vrq870.pdf

Higgs bundles and local systems

© Publications mathématiques de l’I.H.É.S., 1977, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

/pdf/modular-curves-and-the-eisenstein-ideal-395vhnmbh4.pdf

Modular curves and the Eisenstein ideal

We set up the technique of discriminant-forms, which allows us to transfer many results for unimodular symmetric bilinear forms to the nonunimodular case and is convenient in calculations. Further, these results are applied to Milnor's quadratic forms for singularities of holomorphic functions and also to algebraic geometry over the reals. Bibliography: 57 titles.

https://iopscience.iop.org/article/10.1070/IM1980v014n01ABEH001060/pdf

Integral Symmetric Bilinear Forms and Some of Their Applications

In this paper we study linear forms with rational integer coefficients (, ), where the are algebraic numbers satisfying the so-called strong independence condition. In standard notation, we prove an explicit estimate of the form Its novel feature is that it contains no factors of the form .

https://iopscience.iop.org/article/10.1070/IM1998v062n04ABEH000190/pdf

Z.I. Borevich

Papers

Number Theory